Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{1.50\times 10^{5}}{5.0\times 10^{1}}} =\ ?$
Solution: Start by collecting the significands and exponents. $ {\dfrac {{1.50} \times {10^{5}}} {{5.0} \times {10^{1}}} = {\dfrac{1.50}{5.0}} \times {\dfrac{10^{5}}{10^{1}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.30} \times {10^{5 \,-\, 1}}$ $= {0.30} \times {10^{4}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.30}$ is the same as ${3.0 \div 10}$, or ${3.0 \times 10^{-1}}$. $ = {3.0 \times 10^{-1}} \times {10^{4}} $ $ = 3.0 \times 10^{{-1} + {4}} $ $= 3.0\times 10^{3}$